Guided wave propagation in composite laminates using piezoelectric wafer active sensors

Piezoelectric wafer active sensors (PWAS) are lightweight and inexpensive transducers that enable a large class of structural health monitoring (SHM) applications such as: (a) embedded guided wave ultrasonics, i.e., pitch-catch, pulse-echo, phased arrays; (b) high-frequency modal sensing, i.e., electro-mechanical impedance method; and (c) passive detection. The focus of this paper is on the challenges posed by using PWAS transducers in the composite laminate structures as different from the metallic structures on which this methodology was initially developed. After a brief introduction, the paper reviews the PWAS-based SHM principles. It follows with a discussion of guided wave propagation in composites and PWAS tuning effects. Then, the mechanical effect is discussed on the integration of piezoelectric wafer inside the laminate using a compression after impact. Experiments were performed on a glass fiber laminate, employing PWAS to measure the attenuation coefficient. Finally, the paper presents some experimental and multi-physics finite element method (MP-FEM) results on guided wave propagation in composite laminate specimens. AeronAuticAl JournAl october 2013 Volume 117 no 1196 971 Paper No. 3887. Manuscript received 17 July 2012, revised version received 22 March 2013, accepted 22 April 2013. Guided wave propagation in composite laminates using piezoelectric wafer active sensors M. Gresil [email protected] V. Giurgiutiu Department of Mechanical Engineering University of South Carolina, Columbia South Carolina USA 972 the AeronAuticAl JournAl october 2013 NOMENCLATURE A0 first antisymmetric mode Ak amplitude of the partial waves in the kth layer in the global matrix method [C] damping matrix Dj electrical displacement vector, C/m 2 dijkl piezoelectric coupling constant, m/V Cijkl elasticity tensor C stiffness matrix of the composite layer in global co-ordinates, Pa C' stiffness matrix of the composite layer in global co-ordinates, Pa cc coefficient of critical damping Cg group velocity, ms –1 [Cp] piezoelectric stiffness matrix Ek electric field tensor, V/m E1 axial modulus, Pa E2 transverse modulus, Pa [ep] piezoelectric matrix f frequency, Hz J Joules kI attenuation coefficient of the viscoelastic medium, Np {F} force vector [K] stiffness matrix [K] dielectric conductivity. {K} piezoelectric coupling matrix {L} vector of nodal, surface and body charges [M] structural mass matrix S0 first symmetric mode Sij mechanical strain tensor Sijkl mechanical compliance under constant field, m /N t time, s Tkl mechanical stress tensor Ui displacement amplitudes, m u displacement, m un amplitude of vibration after n cycles {u} vector of nodal displacement vn velocity tensor for the nth guided wave mode, ms –1 {v} vector of electric potential αm mass proportionality coefficient βk stiffness proportionality coefficient ζ damping ratio [εp] dielectric matrix εjk dielectric permittivity under constant mechanical stress, F/m ρ density ξ wave number σij stress tensor ω circular frequency, Hz Gresil et al Guided wAVe propAGAtion in composite lAminAte mAteriAl usinG piezoelectric... 973 1.0 INTRODUCTION Structural health monitoring (SHM) is an emerging technology with multiple applications in the evaluation of critical structures. The goal of SHM research is to develop a monitoring methodology that is capable of detecting and identifying, with minimal human intervention, various damage types during the service life of the structure. In the literature, many publications dealing with the propagation of guided waves in a harmonic or transient excitation can be found. The simplest case concerns that of a healthy environment that is to say without damage, simple geometry, and made of homogeneous isotropic materials. This case was treated by classical such as Lamb and Viktorov. Auld used the method of superposition of partial waves to solve the Lamb waves problem. Other researchers have used other methods to describe the Lamb waves. Achenbach determined the displacement components in terms of thickness motion superimposed on a membrane carrier wave which defines the propagation along the plate. The advantage of this technique is that the movement of the membrane can be determined independently. Achenbach and Xu developed this technique for the case of a point source of harmonic pressure applied either to the surface or within a plate. This technique was also used for the case of an axisymmetric harmonic source. Hayachi and Endoh calculated and visualised the propagation of Lamb waves using a hybrid method. Moreno et al used the Fourier transform to study the propagation of a pressure pulse in an isotropic elastic plate. Other studies have been developed for the case of anisotropic media. Rose treated the problem of the influence of the source on the propagation of Lamb waves in the three space directions. He used an analytical technique based on the asymptotic approximation to evaluate the far-field displacements in a composite plate. Nayfeh and Chimenti studied the problem of Lamb waves dispersion curves in anisotropic plates, while Liand and Thompson determined the Lamb waves dispersion curves in monoclinic symmetry and also for higher symmetries. All propagation media mentioned above are monolayers. However, in recent years, studies of multilayer materials have also been developed. Nayfeh used the transfer matrix method to solve the problem of propagation of Lamb waves in an anisotropic layered material. In a more recent article, Lowe gives a summary review of existing techniques for modeling ultrasonic wave propagation in multilayer structures. This article also includes details of the transfer matrix and global matrix methods. Pierce et al determined the characteristics of Lamb waves in the case of structures composed of layers of composite materials and hybrid type laser excitation. Liu et al studied the case of the propagation of Lamb waves by multi-element transducers. As we can see, the list of research on the propagation, excitation and reception of Lamb waves is long and is far from exhaustive. Guided waves open the way for SHM on long distance, with the hope of developing self-sensing structures of large dimensions without necessarily increasing the number of sensors and thus without increasing the complexity of the monitoring system. For guided wave in composite laminate structure, there are advantages in using small piezoelectric wafer active sensors (PWAS) that can be embedded inside the laminate composite. In fact, there are two possibilities of integration PWAS transducers for SHM systems: (i) bonded on the composite structure; and (ii) embedded into the composite laminate structure. Besides the problems inherent in this integration, such as connectivity, the problem of integration raises two points that must be answered: (i) monitoring the integrity of the structure and sensors; and (ii) robustness of the method against anomalies in the integration of sensors. Indeed, the insertion of a foreign element in a host material has the immediate effect of locally modifying the mechanical behavior of the structure. It is therefore imperative to study the effect of the insertion of the sensor 974 the AeronAuticAl JournAl october 2013 on the mechanical properties of the structure and vice versa. Reference may be made to the thesis of Blanquet which focused exclusively in this study. On this subject, Lin and Chang conducted mechanical tests on the impact of integrating piezoelectric sensor network in the middle of a composite material. Bending tests, shear tests, short beam bending tests and compression tests were performed on different samples. These tests showed that there is no noticeable effect on the integrity of the structure. This proves that this system can be used without degrading the mechanical properties of the structure. However, to ensure that there is really no degradation, we conduct a study on the mechanical effect of such integration on compression after impact. Damages mechanisms in composite material subjected to impact are very complex and can be predicted by finite element. In this study, the goal is not to proposed a SHM system to detect and quantify the damaged due to impact but to study the effect of the insertion of PWAS transducer in a composite material. The present paper presents and discusses the challenges and opportunities related to the use of piezoelectric wafer active sensor (PWAS) transducers in generating and sensing guided waves in composite laminate structure. The multi-physics finite element method (MP-FEM) implementation allows for the consideration of the contributions of the active material, and the laminate structure. After a brief introduction, the paper reviews the PWAS-based SHM principles. It follows with a discussion of guided wave propagation in composites and PWAS tuning effects. Experiments were performed on a glass fiber laminate, employing PWAS to measure the attenuation based on the Rayleigh damping coefficients due to the viscoelasticity of the composite material. Finally, the paper presents some experimental and MP-FEM results on guided wave propagation in composite laminate specimens. The paper ends with summary and conclusion; suggestions for further work are also presented. 2.0 PIEZOELECTRIC WAFER ACTIVE SENSORS (PWAS) PWAS are the enabling technology for active SHM systems. PWAS couple the electrical and mechanical effects (mechanical strain, Sij, mechanical stress, Tkl electrical field, Ek, and electrical displacement Dj) through the tensorial piezoelectric constitutive equations: